Term Definition Figure

Transcription

1 Notes LT Distinguish and apply basic terms of geometry (coplanar, collinear, bisectors, congruency, parallel, perpendicular, etc.) Term Definition Figure collinear on the same line (note: you do not have to be able to see the line, it just needs to be possible to draw one) plane an undefined term thought of as a flat surface extending infinitely along its edges. coplanar on the same plane congruent bisect midpoint angle vertex of an angle identical in shape and size to divide into two congruent pieces the point on a line that is equidistant from both endpoints. The midpoint bisects the segment. two noncollinear rays having a common endpoint the point of intersection of the two rays that form an angle see figures for midpoint and angle bisector

2 congruent angles angles with the same measure angle bisector counterexample a ray that has its endpoint at the vertex of the angle and divides the angle into two congruent angles an example that shows a conjecture to be incorrect or a definition to be inadequate Conjecture: All rectangles are squares. Counterexample: inscribed polygon circumscribed polygon a polygon whose sides are chords of the same circle a polygon whose sides are all tangents of the same circle Name Wording Figure Segment Addition Postulate If A, B, and C are collinear and B is between A and C, then AB + BC = AC Angle Addition Postulate If R lies in the interior of STV, then m STR + m RTV = m STV

3 Notes LT Identify and name segments, lines, and rays. Geometry uses precise definitions, postulates, theorems, and notation. It is important that you pay attention to detail to be as successful as possible in this class. The following notations all mean something different: AB AB BA AB AB One thing to note though is that they all use capital letters. Why? In geometry, capital letters are used to denote points and lower case letters are used for other purposes, as you will see. So, what do these mean? A: point A AB : the line segment with endpoints A and B. This could also be written BA AB : the ray with endpoint A that passes through point B BA : the ray with endpoint B that passes through point A AB : the line that passes through points A and B. The line below could have several legitimate names. AB : the distance between point A and point B AB : the arc (on a circle) with endpoints A and B. With only the endpoints given, this is a minor arc (shorter than a semicircle)

4 Notes LT1.3 - Classify special angle pairs (vertical, linear, complementary, supplementary) and angles (right, acute, obtuse, congruent). Angles Parts of an angle: sides: vertex: Naming angles: Types of angles: Measuring an angle: Now, measure these angles:

5 Angle Pairs Complementary Angles Two angles whose measures have a sum of 90 Supplementary Angles Two angles whose measures have a sum of 180 Vertical Pair of Angles Formed by two intersecting lines Have a common vertex Do not share a side Linear Pair of Angles Share a vertex Share a side Their non-common sides form a line

6 Notes LT Classify triangles (right, acute, obtuse, scalene, equilateral, isosceles) Types of triangles: Acute triangle Right triangle Obtuse triangle Scalene Triangle Isosceles Triangle Equilateral triangle

7 Notes LT Classify polygons and their parts (side, vertex, diagonal, convex/concave, congruency, equiangular, equilateral, regular) Polygons Vocabulary with polygons: diagonal of a polygon a line segment that connects two nonconsecutive vertices perimeter of a polygon the sum of the lengths of its sides equilateral polygon a polygon in which all sides have equal length equiangular polygon a polygon in which all angles have equal measure Classification of polygons: Sides Name 3 triangle 4 quadrilateral 5 pentagon 6 hexagon 7 heptagon 8 octagon 9 nonagon 10 decagon 11 undecagon 12 dodecagon n n-gon regular polygon a polygon that is both equilateral and equiangular Convex vs. concave polygons Convex no diagonal is outside the polygon Concave at least one diagonal is outside the polygon Congruent polygons and notation:

8 Notes LT Classify circles and their parts (radius, chord, diameter, tangent, arc and measure, central angle) Naming a circle: a circle is named using the point at its center. So, P is at right. Vocabulary with circles Chord Diameter Tangent A line segment whose endpoints lie on the circle A chord that passes through the center The longest chord A line that intersects the circle only once Congruent circles Concentric circles Arc Circles that have the same radius Coplanar circles that share the same center Two points on the circle and a continuous part of the circle between the two points.

9 Semicircle Minor arc Major arc An arc of a circle whose endpoints are the endpoints of a diameter. An arc of a circle that is smaller than a semicircle. An arc of a circle that is larger than a semicircle. Central angle An angle with its vertex at the center of the circle, and sides passing through endpoints of an arc Arc measure The same as the measure of the central angle that intercepts the arc. The arc is measured in degrees.